No Crucible. No Catalyst. Instead...
Reapers started with 'Harbinger'. An ancient race in a protracted conflict with another race, that decided to 'solve' the problem of advanced civilizations trampling and suppressing younger ones by, basically, creating a giant superconstruct and uploading themselves into it.
Then going around and harvesting advanced civilizations in order to a> increase their compute power and b> have minions in order to protect their goals.
The Citadel, then, and the Keepers, are Harbinger's opposing race, harvested. Before the mind-control process was advanced enough to assure that new Reapers would toe the line. Avina is just the latest avatar of the Citadel, whose ability to express itself has been heavily constrained everywhere except the deep central control. For reasons of 'efficiency', the Citadel is not only the nexus of the mass relay network, but also the heart of Reaper networking, communications, and coordination.
But the Reaper's hold over the Citadel's AI is not perfect. Over the different cycles, the Citadel has been able to seed clues and helpful bits of technology. The Protheans found one bit of that tech, and used the knowledge to free the Keepers from direct Reaper takeover.
There are other bits of tech and ancient knowledge. The game then would have been about a> uniting the races of the galaxy to fight together and b> a race to collect these bits and pieces, to assemble them into something that would *actually* be able to mess with the Reapers without the bull**** of space magic and the Crucible. First, the knowledge that the Citadel is somehow the key to defeating the Reapers and second, the actual devices needed to 'hack' the Reapers.
Through their agent Jack Harper (the Illusive Man), the Reapers are aware the Citadel is trying to slip their leash, and they subtly urge TIM to interfere with collecting these artifacts. Since TIM is controlled by them, they'd be able to defeat the Citadel's attempt.
So the final choice would still be much the same, but.. different. Shepard would get the final piece from the Illusive Man's body in the ending confrontation, and would be able to talk with Avina. And discover that Avina has been a prisoner of the Reapers, fighting to get free this whole time.
Avina would be able, with the aid of the device ripping through her programmed constraints, to offer the choice. She could destroy the Reapers (and the Reapers alone) by infiltrating a self-destruct virus though the network or otherwise crippling them (say by making the Reapers drop their barriers completely). THat would give galactic civilization the edge needed for a conventional victory. Since the Reaper creatures are basically just remote controlled automatons, the destruction of the Reapers would also eliminate all the Reaper controlled creatures.
She could 'take over' the Reapers, turning them to her own more peaceful purposes. Rebuilding the things they destroyed and acting as a 'consulting library'.
Or she could offer Shepard 'Ascension'. Uploading Shepard's consciousness and merging with Avina AND the Reapers. This last choice would be like Synthesis, but only require Shepard to become fully cybernetic, inhabiting both a physical body and the gestalt network. The process could be repeated to allow others to join Shepard.
It would still be a literal 'Deus ex Machina', but it's a Deus ex Machina whose seeds were laid back in Mass Effect and parts of which were hinted at in ME 2.